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Couple wins millions using lottery loophole

treydey 7y ago
Can anyone explain the strategy like I'm 5? I'm confused by his answer.
- bsaul 7y ago
  Even weirder is the statement that the State that organized the lottery made more money thanks to them buying massive amount of tickets ( or maybe it was the publicity around the first newspaper article that triggered more interest, and so more participant in general ?)
  - Piskvorrr 7y ago
    I understand the opposite: the State didn't lose any money, (but didn't make any money from these people winning, either); it made money from lottery as usual, but not from these people. (There's an implication that more people in general bought tickets, didn't win, and so the organizer made money from those - but it's not entirely clear.)
    - thaumasiotes 7y ago
      The state makes money from every ticket purchased. The lottery simply pays out a fixed percentage of ticket revenue. More ticket sales means more money to the state, regardless of whether those tickets, when purchased, had an expected positive or negative return.
      - pliny 7y ago
        If the ticket has an expected positive return for the buyer, then the state must be losing money.
        progval 7y ago
        It has an expected positive return only on the days there was a Rolldown. Money came from people who played on days there wasn't one.
        zawerf 7y ago
        I feel like mathematically, you must be right. One of the sides must be calculating their expected value wrong. For example I can offer to pay a $3 jackpot (split across winners) for a $1 game for guessing heads or tails. If more than 3 people play the game, I make money. For each player, the naive way to calculate expected return is $3 * 0.5 + $0 * 0.5 - $1 = $0.5. So the players also think they are making money. But once you account for jackpot splitting, that "expected value" isn't positive anymore. To calculate this correctly, the player (who has less information) need some way to model the distribution of the number of other players.
        thaumasiotes 7y ago
        > mathematically, you must be right. One of the sides must be calculating their expected value wrong. He isn't right. The state doesn't work with expected values in any way. Money comes in via ticket sales, some of it goes into the state budget, the rest goes out as lottery payouts. There is no element of chance in any of that. As you point out here and I point out elsewhere, the expected value of a ticket for the purchaser depends on the total number of tickets sold, which has been mostly elided from the discussion. In fact, it's mostly irrelevant as to this past event; at the actual ticket volumes, returns really were positive on the days in question.
        pliny 7y ago
        The way the game is presented in the article is that the low payout numbers are fixed (so a 3 match on a given rolldown game pays out $50 regardless of how many winners there are). This is consistent with the state lotteries I know. In this scenario every ticket sold causes the state to lose money, on average.
        7y ago
      - deleted 7y ago
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    - M2Ys4U 7y ago
      Are state lottery ticket purchases taxed? That'd also bring in a chunk of change.
  - jarfil 7y ago
    That is correct: since these were not usual players who abstained from playing, but rather casual players who bought extra tickets just on rolldown, while the State got a cut from every ticket sale, they were effectively pouring extra money into the lottery, increasing the State's income. Even if they re-invested their previous winnings, that would be twice (or more) that the State would get its cut from the same money, still increasing its income.
  - Double_a_92 7y ago
    The money was "stolen" from the person that would have won the jackpot. The maximum jackpot was just smaller, it didn't make a difference to the lottery who actually won that money. They could say that the jackpot will be split among everyone that has exactly one number right in the next round, and still make profit.
- Piskvorrr 7y ago
  If nobody wins the big jackpot ("guess all the numbers") for some time, parts of it are given to the smaller winners ("guess a few of the numbers"). In this case, which happened once in a while, it became more likely that you'll win more than you have bet. Usually this means you'll win some $50; they have bet many, many times, and won $50 times many. Doesn't work any more, rules have changed so this way of winning was removed.
  - tylerhou 7y ago
    But which set of tickets do you buy?
    - Piskvorrr 7y ago
      From the article, it seems that it doesn't matter, they're random. (Or were random, apparently it's over now, doesn't matter.) To make up an example: Let's say that betting $1 in some way has a 4% chance of winning, and the payout is 20x bet, so if you win on one ticket, you get $20. So, you buy a lot of tickets (say 1000), and you pay $1000. Most of them don't win anything, but 4% of them win $20; $1000 x 4% x 20 = $800; you have won some, but you have $200 less than you started with. Not a good deal. However, if nobody wins the jackpot, it is distributed amongst smaller payouts, which changes the equation: still 4% chance, but payout is now $30. Again, you pay $1000, buy 1000 tickets, most don't win anything, but the 4% that do, you get $1000 x 4% x 30 = $1200. You have $200 more than you started with. Profit! Of course, this will only work if you buy many tickets; buying one or two, you're unlikely to win anything at all. The actual numbers were different in these cases, but the general principle is the same.
      - amelius 7y ago
        That requires a lot of faith in the fairness of the particular lottery.
        loblollyboy 7y ago
        A. Any lotto requires faith. B. Selbee didnt put all his money in initially. C. The parent comment is just explaining a concept w a hypothetical example
- emerongi 7y ago
  The jackpot grows off of people losing money. Once people have lost enough money ($5M), the chances of winning the money with a single ticket are raised, however you can no longer win the whole $5M with a single ticket - the money is now distributed over a larger pool of tickets. After that it becomes a good bet, because you can bet smaller amounts, but still win more than you put in initially - you're profiting off of people who lost money before you.
  - chrismcb 7y ago
    Someone can always win the whole 5M. It is just that if the prize for large enough and no one win, then the amount of the small prizes increased. It was a way to keep the total payout low.
- martin_b 7y ago
  There is a great lecture about it from The Royal Institution https://www.youtube.com/watch?v=kZTKuMBJP7Y https://www.youtube.com/watch?v=kZTKuMBJP7Y
- kickopotomus 7y ago
  It might make a little more sense with the numbers. WinFall was a typical lottery game where you choose 6 of 46 numbers[1]. As with most lottery games, there is a jackpot payout but there are also payouts for matching 3, 4, and 5 of the numbers. The odds breakdown goes like this[2]: Result | Odds ------------- 6 of 6 | 1 in 9,366,819 5 of 6 | 1 in 39028.41 4 of 6 | 1 in 800.58 3 of 6 | 1 in 47.40 2 of 6 | 1 in 6.83 The issue with WinFall is that when the jackpot increased past $5MM, the expected value of the non-jackpot winnings becomes favorable to the player. I.e. a 5-of-6 matching ticket might normally yield $4,000 but may yield >$20,000 for a "Roll-down" game. So if you go out and buy 200,000 tickets for the roll-down game (assuming all tickets are different and numbers are selected at random), you should expect to have 5 5-of-6 tickets, 250 4-of-6 tickets, 4,219 3-of-6 tickets, and 29,283 2-of-6 tickets. The combined winnings of all of those tickets makes it profitable. [1]: https://www.mass.gov/files/documents/2016/08/vv/lottery-cash-winfall-letter-july-2012.pdf https://www.mass.gov/files/documents/2016/08/vv/lottery-cash... [2]: https://en.wikipedia.org/wiki/Lottery_mathematics https://en.wikipedia.org/wiki/Lottery_mathematics
  - em-bee 7y ago
    so in each game the money that is not won is collected in the pool until the pool is bigger than the overall cost for all tickets? and in other games this doesn't work because they are 'winner-takes-all'?
  - treydey 7y ago
    This is what I was looking for! Thanks.
- losvedir 7y ago
  * Expected value of the lottery tickets is normally negative. (You pay $1, you expect on average to get back less than $1). * At a certain point, if the jackpot grows too large, the game switches to a new "windfall" mode where the expected value is actually _positive_ to bleed off the jackpot. (You pay $1, you expect on average to get back more than $1). * The couple and the MIT students only played during the positive expected value times. Overall the game still makes money for the state, it's just it has two distinct regimes, and the people playing during negative-EV essentially bankroll both the state and the positive-EV players.
onetimemanytime 7y ago
$80 BILLION a year in lottery spending, that was shocking to me. Only 30 some countries have bigger yearly budgets. https://en.wikipedia.org/wiki/List_of_countries_by_government_budget https://en.wikipedia.org/wiki/List_of_countries_by_governmen...
- smcl 7y ago
  Remember that you can look at a lot of data on the US like this and come up with seemingly shocking figures, simply because of the huge population of the USA and their higher than average disposable income. I bet if you looked at other things like total amount spent on other optional/nonessential items - chewing gum or fabric softener, for example - you'd end up with a dollar value in excess of what many governments spend :-)
  - onetimemanytime 7y ago
    Oh, I know. Our GDP does it. If US can spend $80 Billion on lottery tickets imagine what we can spend to win a war. Makes you think more than twice before poking the bear.
  - rzzzt 7y ago
    The chewing gum market is a bit smaller (but impressive nonetheless), 110-ish countries have revenues comparable to sales in North America: https://www.foodbusinessnews.net/articles/13098-chewing-gum-sales-estimated-to-hit-4-billion-in-2018 https://www.foodbusinessnews.net/articles/13098-chewing-gum-... https://www.statista.com/topics/1841/chewing-gum/ https://www.statista.com/topics/1841/chewing-gum/
- onion2k 7y ago
  It's very common for people who win small prizes to 'reinvest' their winnings though. Someone who spends $5 and wins $25 might then just buy $25 of tickets with that win. If they're playing online that money never really exists - it's just an account balance in a database going up and down.
- chrshawkes 7y ago
danielecook 7y ago
Love hearing stories like this where people gained because of some loophole. Does anyone know if there is a compilation somewhere of these? See also: https://www.businessinsider.com/us-mint-ends-the-dollar-coin-scam-for-airline-miles-2011-7?r=US&IR=T https://www.businessinsider.com/us-mint-ends-the-dollar-coin...
- yomly 7y ago
  Look up Joan Ginther - ex-Stanford statistician and she won scratchcard lotteries multiple times (I seem to recall by arbing non-uniform geographical distribution of winning cards). Unfortunately I can't find a technically satisfying article and don't have ability to find one right now...
  - deleted 7y ago
    [deleted]
- mrspuratic 7y ago
  Irish Lottery, 1992, brute force - you could purchase all ~2M combinations for < IR£1M . The company played dirty when they realised what was happening, then later changed the game when they'd finished the forehead slapping: https://en.wikipedia.org/wiki/National_Lottery_%28Ireland%29#History_of_Lotto https://en.wikipedia.org/wiki/National_Lottery_%28Ireland%29...
- js2 7y ago
  “A nationwide reporting adventure tracks improbably frequent lottery winners”: https://www.cjr.org/united_states_project/lottery-winners-foia-reporting.php https://www.cjr.org/united_states_project/lottery-winners-fo... Discussion: https://news.ycombinator.com/item?id=15262440 https://news.ycombinator.com/item?id=15262440
- giarc 7y ago
  There is a story similar to the dollar coin gig to earn reward miles. A long time ago when plastic gift cards were first a thing, stores didn't have a way to update the balance. The scheme would be to buy a $100 gift card from Walmart using your credit card (getting the miles). You would then use the gift card to buy a $0.35 pack of gum. Since the store couldn't update the balance, they would give you cash as change. You could then just deposit the change to your bank and pay off the credit card. Rinse, repeat. So for $0.35, you could get $100 in equivalent reward miles. Now stores have changed, they can now update balances on the card and therefore won't issue cash as change.
deleted 7y ago
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MeteorMarc 7y ago
I just wonder, do you have to think very high about yourself to play such a game and enjoy it? Or very low? I just can not imagine myself feeling good about this. Of course, the feeling dumbs a bit: compare the feelings you had after using your first illegally copied floppy disk or mp3 track and the later ones, but still.
- barking 7y ago
  I'd enjoy it very much and not feel bad at all.
- chrismcb 7y ago
  Why would you feel bad? What woukd you have down that was wrong? You aren't taking money from anyone else.
  - tantalor 7y ago
    You are taking money from the prize pool, i.e. payouts for future winners.
    - chrismcb 7y ago
      You, and everyone else. That is the rule of the game. You aren't doing anything wrong. By that logic, any money winner is taking payours from future winners.
      - tantalor 7y ago
        > You aren't doing anything wrong. That's debatable. Lotteries are supposed to be completely up to chance. If by your own ingenuity you exploit a weakness then you are tipping the scales in your favor, which is unfair to less clever players. It's basically the tragedy of the commons; everyone has the same chance of winning, but only you know you can safely risk more and win more, lessening the winning of others.
        7y ago
Slartie 7y ago
When I read this kind of stories about US lotteries (and there seem to be several of this kind of stories going around), I always wonder how on earth it is possible for so many cases of failed lottery rule design to exist in the first place, and for those clear failures to persist for so long. Did no one notice that the lottery always lost huge sums of money during the Rolldown draws, while it gained money on normal draws (as it should always be the case)? No one noticed that certain convenience stores suddenly sold hundreds of thousands worth of tickets in these draws, while most other stores sold a normal amount?
- caf 7y ago
  Long before that point, lotteries that decide to innovate in game design don't have a professional actuary on the staff to run the ruler over the designs?
  - soneil 7y ago
    That's the weird part for me. Surely inventing a whole new game mechanic, must be their industry's version of rolling your own encryption?
    - mrosett 7y ago
      Well, that also seems like something state governments would do.
- ilamont 7y ago
  These lotteries are usually run by state commissions, staffed by career bureaucrats and sometimes led by appointees. I don't think there's a deep well of talent that is familiar with how to implement robust monitoring, security, and optimization systems.
- kd5bjo 7y ago
  The lottery’s and retailers’ profits are each a fixed amount of the ticket price, and the rest goes into the prize pool. They don’t lose any money unless they commit to paying more prize money than they allocated to the pool. Jackpots are explicitly a (large) fraction of the unallocated award funds and so cannot make the lottery operation insolvent— only an excess of fixed-value awards can do that. In fact, the increased sales on rolldown draws just mean more profit for the operators and reduce their biggest risk, which is something happening to the stored funds used to pay out prizes.
sureaboutthis 7y ago
I first read about these people a year or so ago so CBS "news" has finally caught up.
ocfnash 7y ago
A wonderful account of this is given in Ellenberg's "How Not to Be Wrong": https://en.wikipedia.org/wiki/How_Not_to_Be_Wrong https://en.wikipedia.org/wiki/How_Not_to_Be_Wrong I highly recommend the book; it is a popular mathematics book, written by a real mathematician, discussing some real mathematics, with an engaging style.
- gauravjain13 7y ago
  Video: https://youtu.be/kZTKuMBJP7Y https://youtu.be/kZTKuMBJP7Y
RickJWagner 7y ago
Good for them! Thinking is rewarded.
Xunxi 7y ago
They were featured on 60 minutes twice, including last night. The rendering on Microsoft News is off! You can see the entire video here. https://www.cbsnews.com/news/jerry-and-marge-selbee-how-a-retired-couple-won-millions-using-a-lottery-loophole-60-minutes-2019-06-09/ https://www.cbsnews.com/news/jerry-and-marge-selbee-how-a-re...
js2 7y ago
Previous discussion a year ago: https://news.ycombinator.com/item?id=16494280 https://news.ycombinator.com/item?id=16494280 On this submission: http://highline.huffingtonpost.com/articles/en/lotto-winners/ http://highline.huffingtonpost.com/articles/en/lotto-winners...
- joshstrange 7y ago
  This is a MUCH better writeup than this recently submitted link. I remember reading it at the time, very well done.
- fragmede 7y ago
  The original Mass gaming commission report is floating around out there, if anyone is looking for additional reading on this subject, though it is of limited interest, outside of a select few MIT students and a couple from Michigan.
coldcode 7y ago
I wish lotteries handed out many $1M prizes instead of giving $250M to one person. People understand what to do with $1M (I think) but most people are ruined by $250M.
- wvenable 7y ago
  The reason they don't do that is marketing; more people play for big jackpot. I think even saying there might 250 $1 million winners this week isn't as big of an enticement.
  - indigodaddy 7y ago
    Exactly, they would never sell anywhere close to the amount of tickets as they do for the single-winner lump sums that swell to ridiculous amounts. So they wouldn't have the necessary incoming ticket sales to be able to do the 250 $1 million winners.
    - Consultant32452 7y ago
      Around here when the jackpots get high enough you actually find really long lines just to buy tickets. No one lines up to buy the scratch offs with much better odds of winning $1 million.
  - vonzeppelin 7y ago
    When the jackpot reached a certain amount, say 500 million, they could switch from a winner takes all to essentially a raffle with 500 winners. I think it would greatly increase the number of tickets purchased when the threshold was met.
    - dawnerd 7y ago
      Isn't that kinda what the Windfall game did more or less?
    - lukeholder 7y ago
      This is what the windfall game in the article did. They were smart enough to buy as many tickets as possible during this raffle.
twic 7y ago
The paper's reporting revealed that two groups were dominating Cash Winfall: the Selbee gang from Evart, Michigan, and their competition, a syndicate led by math majors from MIT, the Massachusetts Institute of Technology. These were kids young enough to be the Selbees' grandchildren. Incredibly, the MIT group bet between $17 and $18 million on Cash Winfall over a seven-year period, earning at least $3.5 million in profits. Almost the exact same rate of return as the Selbees. A nice illustration of the fact that there is only one mathematics, and it's equally available to everyone!
- bhl 7y ago
  Based on the numbers alone, that's about a 20% return for the MIT group, for an annualized return (not considering compound interest) of less than 3% per year. Does this suggest that those trying to game the lottery should just turn to investing in the market? It's amusing to see that the market, which is less structured in probability and more volatile, outperforms the lottery in this aspect.
  - mNovak 7y ago
    The money is only tied up for a few days of the year while they hold tickets though, the rest of the time it could be sitting in a suitably liquid investment. In that sense it far outperforms the market.
  - bcbrown 7y ago
    That doesn't mean they had that amount of capital under investment. If you bet $10 every week, and every week you win $11, at the end of the year you've bet $520 and made a profit of $52. But you never had more than $10 "invested". If that $18 million was evenly spread out over 7 years, it would be close to $50k/week, or $215k/month. Those are probably more accurate amounts of working capital for calculating ROI.
    - adrianmonk 7y ago
      Yeah, the way the article phrased it, I have a feeling this is a useless statistic like the sum total of all the money spent on tickets.
unixhero 7y ago
Great story.. but extremely shitty interviewer in my view.
jedberg 7y ago
To all the folks saying, "how did the State not know the odds?", a lot of gambling games come out without anyone running the odds. A great example is blackjack switch [0]. The game was invented by an ex-gambler and he never really knew the odds of the game. He just convinced some casinos to try it and would advertise what their average take was. Because most people are bad at math and wouldn't play well, it was always bigger than the actual house advantage anyway. It was only years later that someone finally ran the numbers and figured out the actual house advantage of the game [1], but no one cared because everyone who had a table was making money on it. Even with regular blackjack, the casinos always make way more than the statistical house advantage because people play poorly. It was probably the same deal here. The State didn't care what they actual odds were, they just cared that they were making money on it. [0] https://en.wikipedia.org/wiki/Blackjack_Switch https://en.wikipedia.org/wiki/Blackjack_Switch [1] https://wizardofodds.com/games/blackjack/switch/ https://wizardofodds.com/games/blackjack/switch/
- qtplatypus 7y ago
  I work in the gambling industry and live in au. From my perspective this is super strange. By law vendors have to publish the odd (and on some games the EV).
  - rwc 7y ago
    Publishing the odds is common. Doing the math on those odds apparently is not.
    - MegaButts 7y ago
      But in order to publish the odds, you have to know the odds. And the only way to know the odds is to do the math, correct? Unless you're making a distinction for determining the odds during optimal play (which makes a lot more sense to me).
      - kijin 7y ago
        Lotteries are required to publish the odds of matching x out of y numbers. Once the design is fixed, this figure does not change. The expected dollar value of a winning ticket, on the other hand, changes every week depending on the number of tickets sold that week as well as the amount of any unclaimed jackpot(s) rolled over from previous weeks. I won't be surprised if state lotteries are not legally required to publish these figures every week. Nobody wants to be held responsible for a precise amount published on Tuesday when a snowstorm on Friday causes ticket sales to plummet. Many states do publish estimates of the jackpot, of course, for advertising purposes. But they're only estimates, and I've never seen estimates of anything other than the jackpot. The Selbees took advantage of smaller winnings that usually go unnoticed.
notfed 7y ago
The title of an article I would never have clicked on if it were not referenced via Hacker News...
deleted 7y ago
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mattdeboard 7y ago
"That was satisfactory." I love that this guy, who is probably, what, 80? 81? pulled off this huge math heist after probably a lifetime spent doing math running a convenience store. I bet it feels great to have that sense of, like, ease with himself in old age, having made a mark on the world in a way that hurt no one and helped a lot of people. He stuck the landing
- gowld 7y ago
  He hurt all the lottery players he beat.
  - zaroth 7y ago
    In fact not. Their winnings did not take a $1 of winnings from anyone else.
  - TallGuyShort 7y ago
    They bet money on a game that somebody else played better.
fewrx 7y ago
Every decade or so some "lottery loophole" like this is discovered, exploited, publicized, and rules are updated to close it. I'm curious to see if another loophole resulting in a massive rework of the lottery system will ever present itself, or if the laws and rules have finally prevented that after the last few.
elamje 7y ago
I really enjoyed this story! The best part is people like to think this loop hole is easy “profit”. No one pointed out the fact that they would go on 10 day benders buying/sorting/etc. to get the profit! Even this loop hole for easy profit was incredibly arduous in manual labor.
seventhtiger 7y ago
I was wondering how both these syndicates and the state we winning. I think I understand now. Lotteries are zero sum games so no extra money is being created. All ticket purchases either go to the state or the winners. So if the players have a positive return how can the state also be winning? The players have a positive return only for the rollover round. The players have a negative return for all other rounds, where the state makes its money, and the syndicates don't play. So the people who lost are all the suckers who played in non-rollover rounds.
bamurphymac1 7y ago
Great story. Now they should go make another million or two selling the movie rights!

Can anyone explain the strategy like I'm 5? I'm confused by his answer.

bsaul 7y ago
Even weirder is the statement that the State that organized the lottery made more money thanks to them buying massive amount of tickets ( or maybe it was the publicity around the first newspaper article that triggered more interest, and so more participant in general ?)
- Piskvorrr 7y ago
  I understand the opposite: the State didn't lose any money, (but didn't make any money from these people winning, either); it made money from lottery as usual, but not from these people. (There's an implication that more people in general bought tickets, didn't win, and so the organizer made money from those - but it's not entirely clear.)
  - thaumasiotes 7y ago
    The state makes money from every ticket purchased. The lottery simply pays out a fixed percentage of ticket revenue. More ticket sales means more money to the state, regardless of whether those tickets, when purchased, had an expected positive or negative return.
    - pliny 7y ago
      If the ticket has an expected positive return for the buyer, then the state must be losing money.
      - progval 7y ago
        It has an expected positive return only on the days there was a Rolldown. Money came from people who played on days there wasn't one.
      - zawerf 7y ago
        I feel like mathematically, you must be right. One of the sides must be calculating their expected value wrong. For example I can offer to pay a $3 jackpot (split across winners) for a $1 game for guessing heads or tails. If more than 3 people play the game, I make money. For each player, the naive way to calculate expected return is $3 * 0.5 + $0 * 0.5 - $1 = $0.5. So the players also think they are making money. But once you account for jackpot splitting, that "expected value" isn't positive anymore. To calculate this correctly, the player (who has less information) need some way to model the distribution of the number of other players.
        thaumasiotes 7y ago
        > mathematically, you must be right. One of the sides must be calculating their expected value wrong. He isn't right. The state doesn't work with expected values in any way. Money comes in via ticket sales, some of it goes into the state budget, the rest goes out as lottery payouts. There is no element of chance in any of that. As you point out here and I point out elsewhere, the expected value of a ticket for the purchaser depends on the total number of tickets sold, which has been mostly elided from the discussion. In fact, it's mostly irrelevant as to this past event; at the actual ticket volumes, returns really were positive on the days in question.
        pliny 7y ago
        The way the game is presented in the article is that the low payout numbers are fixed (so a 3 match on a given rolldown game pays out $50 regardless of how many winners there are). This is consistent with the state lotteries I know. In this scenario every ticket sold causes the state to lose money, on average.
        7y ago
    - deleted 7y ago
      [deleted]
  - M2Ys4U 7y ago
    Are state lottery ticket purchases taxed? That'd also bring in a chunk of change.
- jarfil 7y ago
  That is correct: since these were not usual players who abstained from playing, but rather casual players who bought extra tickets just on rolldown, while the State got a cut from every ticket sale, they were effectively pouring extra money into the lottery, increasing the State's income. Even if they re-invested their previous winnings, that would be twice (or more) that the State would get its cut from the same money, still increasing its income.
- Double_a_92 7y ago
  The money was "stolen" from the person that would have won the jackpot. The maximum jackpot was just smaller, it didn't make a difference to the lottery who actually won that money. They could say that the jackpot will be split among everyone that has exactly one number right in the next round, and still make profit.
Piskvorrr 7y ago
If nobody wins the big jackpot ("guess all the numbers") for some time, parts of it are given to the smaller winners ("guess a few of the numbers"). In this case, which happened once in a while, it became more likely that you'll win more than you have bet. Usually this means you'll win some $50; they have bet many, many times, and won $50 times many. Doesn't work any more, rules have changed so this way of winning was removed.
- tylerhou 7y ago
  But which set of tickets do you buy?
  - Piskvorrr 7y ago
    From the article, it seems that it doesn't matter, they're random. (Or were random, apparently it's over now, doesn't matter.) To make up an example: Let's say that betting $1 in some way has a 4% chance of winning, and the payout is 20x bet, so if you win on one ticket, you get $20. So, you buy a lot of tickets (say 1000), and you pay $1000. Most of them don't win anything, but 4% of them win $20; $1000 x 4% x 20 = $800; you have won some, but you have $200 less than you started with. Not a good deal. However, if nobody wins the jackpot, it is distributed amongst smaller payouts, which changes the equation: still 4% chance, but payout is now $30. Again, you pay $1000, buy 1000 tickets, most don't win anything, but the 4% that do, you get $1000 x 4% x 30 = $1200. You have $200 more than you started with. Profit! Of course, this will only work if you buy many tickets; buying one or two, you're unlikely to win anything at all. The actual numbers were different in these cases, but the general principle is the same.
    - amelius 7y ago
      That requires a lot of faith in the fairness of the particular lottery.
      - loblollyboy 7y ago
        A. Any lotto requires faith. B. Selbee didnt put all his money in initially. C. The parent comment is just explaining a concept w a hypothetical example
emerongi 7y ago
The jackpot grows off of people losing money. Once people have lost enough money ($5M), the chances of winning the money with a single ticket are raised, however you can no longer win the whole $5M with a single ticket - the money is now distributed over a larger pool of tickets. After that it becomes a good bet, because you can bet smaller amounts, but still win more than you put in initially - you're profiting off of people who lost money before you.
- chrismcb 7y ago
  Someone can always win the whole 5M. It is just that if the prize for large enough and no one win, then the amount of the small prizes increased. It was a way to keep the total payout low.
martin_b 7y ago
There is a great lecture about it from The Royal Institution https://www.youtube.com/watch?v=kZTKuMBJP7Y https://www.youtube.com/watch?v=kZTKuMBJP7Y
kickopotomus 7y ago
It might make a little more sense with the numbers. WinFall was a typical lottery game where you choose 6 of 46 numbers[1]. As with most lottery games, there is a jackpot payout but there are also payouts for matching 3, 4, and 5 of the numbers. The odds breakdown goes like this[2]: Result | Odds ------------- 6 of 6 | 1 in 9,366,819 5 of 6 | 1 in 39028.41 4 of 6 | 1 in 800.58 3 of 6 | 1 in 47.40 2 of 6 | 1 in 6.83 The issue with WinFall is that when the jackpot increased past $5MM, the expected value of the non-jackpot winnings becomes favorable to the player. I.e. a 5-of-6 matching ticket might normally yield $4,000 but may yield >$20,000 for a "Roll-down" game. So if you go out and buy 200,000 tickets for the roll-down game (assuming all tickets are different and numbers are selected at random), you should expect to have 5 5-of-6 tickets, 250 4-of-6 tickets, 4,219 3-of-6 tickets, and 29,283 2-of-6 tickets. The combined winnings of all of those tickets makes it profitable. [1]: https://www.mass.gov/files/documents/2016/08/vv/lottery-cash-winfall-letter-july-2012.pdf https://www.mass.gov/files/documents/2016/08/vv/lottery-cash... [2]: https://en.wikipedia.org/wiki/Lottery_mathematics https://en.wikipedia.org/wiki/Lottery_mathematics
- em-bee 7y ago
  so in each game the money that is not won is collected in the pool until the pool is bigger than the overall cost for all tickets? and in other games this doesn't work because they are 'winner-takes-all'?
- treydey 7y ago
  This is what I was looking for! Thanks.
losvedir 7y ago
* Expected value of the lottery tickets is normally negative. (You pay $1, you expect on average to get back less than $1). * At a certain point, if the jackpot grows too large, the game switches to a new "windfall" mode where the expected value is actually _positive_ to bleed off the jackpot. (You pay $1, you expect on average to get back more than $1). * The couple and the MIT students only played during the positive expected value times. Overall the game still makes money for the state, it's just it has two distinct regimes, and the people playing during negative-EV essentially bankroll both the state and the positive-EV players.

$80 BILLION a year in lottery spending, that was shocking to me. Only 30 some countries have bigger yearly budgets. https://en.wikipedia.org/wiki/List_of_countries_by_government_budget https://en.wikipedia.org/wiki/List_of_countries_by_governmen...

smcl 7y ago
Remember that you can look at a lot of data on the US like this and come up with seemingly shocking figures, simply because of the huge population of the USA and their higher than average disposable income. I bet if you looked at other things like total amount spent on other optional/nonessential items - chewing gum or fabric softener, for example - you'd end up with a dollar value in excess of what many governments spend :-)
- onetimemanytime 7y ago
  Oh, I know. Our GDP does it. If US can spend $80 Billion on lottery tickets imagine what we can spend to win a war. Makes you think more than twice before poking the bear.
- rzzzt 7y ago
  The chewing gum market is a bit smaller (but impressive nonetheless), 110-ish countries have revenues comparable to sales in North America: https://www.foodbusinessnews.net/articles/13098-chewing-gum-sales-estimated-to-hit-4-billion-in-2018 https://www.foodbusinessnews.net/articles/13098-chewing-gum-... https://www.statista.com/topics/1841/chewing-gum/ https://www.statista.com/topics/1841/chewing-gum/
onion2k 7y ago
It's very common for people who win small prizes to 'reinvest' their winnings though. Someone who spends $5 and wins $25 might then just buy $25 of tickets with that win. If they're playing online that money never really exists - it's just an account balance in a database going up and down.
chrshawkes 7y ago

danielecook 7y ago

Love hearing stories like this where people gained because of some loophole. Does anyone know if there is a compilation somewhere of these? See also: https://www.businessinsider.com/us-mint-ends-the-dollar-coin-scam-for-airline-miles-2011-7?r=US&IR=T https://www.businessinsider.com/us-mint-ends-the-dollar-coin...

yomly 7y ago
Look up Joan Ginther - ex-Stanford statistician and she won scratchcard lotteries multiple times (I seem to recall by arbing non-uniform geographical distribution of winning cards). Unfortunately I can't find a technically satisfying article and don't have ability to find one right now...
- deleted 7y ago
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mrspuratic 7y ago
Irish Lottery, 1992, brute force - you could purchase all ~2M combinations for < IR£1M . The company played dirty when they realised what was happening, then later changed the game when they'd finished the forehead slapping: https://en.wikipedia.org/wiki/National_Lottery_%28Ireland%29#History_of_Lotto https://en.wikipedia.org/wiki/National_Lottery_%28Ireland%29...
js2 7y ago
“A nationwide reporting adventure tracks improbably frequent lottery winners”: https://www.cjr.org/united_states_project/lottery-winners-foia-reporting.php https://www.cjr.org/united_states_project/lottery-winners-fo... Discussion: https://news.ycombinator.com/item?id=15262440 https://news.ycombinator.com/item?id=15262440
giarc 7y ago
There is a story similar to the dollar coin gig to earn reward miles. A long time ago when plastic gift cards were first a thing, stores didn't have a way to update the balance. The scheme would be to buy a $100 gift card from Walmart using your credit card (getting the miles). You would then use the gift card to buy a $0.35 pack of gum. Since the store couldn't update the balance, they would give you cash as change. You could then just deposit the change to your bank and pay off the credit card. Rinse, repeat. So for $0.35, you could get $100 in equivalent reward miles. Now stores have changed, they can now update balances on the card and therefore won't issue cash as change.

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MeteorMarc 7y ago

I just wonder, do you have to think very high about yourself to play such a game and enjoy it? Or very low? I just can not imagine myself feeling good about this. Of course, the feeling dumbs a bit: compare the feelings you had after using your first illegally copied floppy disk or mp3 track and the later ones, but still.

barking 7y ago
I'd enjoy it very much and not feel bad at all.
chrismcb 7y ago
Why would you feel bad? What woukd you have down that was wrong? You aren't taking money from anyone else.
- tantalor 7y ago
  You are taking money from the prize pool, i.e. payouts for future winners.
  - chrismcb 7y ago
    You, and everyone else. That is the rule of the game. You aren't doing anything wrong. By that logic, any money winner is taking payours from future winners.
    - tantalor 7y ago
      > You aren't doing anything wrong. That's debatable. Lotteries are supposed to be completely up to chance. If by your own ingenuity you exploit a weakness then you are tipping the scales in your favor, which is unfair to less clever players. It's basically the tragedy of the commons; everyone has the same chance of winning, but only you know you can safely risk more and win more, lessening the winning of others.
      - 7y ago

Slartie 7y ago

When I read this kind of stories about US lotteries (and there seem to be several of this kind of stories going around), I always wonder how on earth it is possible for so many cases of failed lottery rule design to exist in the first place, and for those clear failures to persist for so long. Did no one notice that the lottery always lost huge sums of money during the Rolldown draws, while it gained money on normal draws (as it should always be the case)? No one noticed that certain convenience stores suddenly sold hundreds of thousands worth of tickets in these draws, while most other stores sold a normal amount?

caf 7y ago
Long before that point, lotteries that decide to innovate in game design don't have a professional actuary on the staff to run the ruler over the designs?
- soneil 7y ago
  That's the weird part for me. Surely inventing a whole new game mechanic, must be their industry's version of rolling your own encryption?
  - mrosett 7y ago
    Well, that also seems like something state governments would do.
ilamont 7y ago
These lotteries are usually run by state commissions, staffed by career bureaucrats and sometimes led by appointees. I don't think there's a deep well of talent that is familiar with how to implement robust monitoring, security, and optimization systems.
kd5bjo 7y ago
The lottery’s and retailers’ profits are each a fixed amount of the ticket price, and the rest goes into the prize pool. They don’t lose any money unless they commit to paying more prize money than they allocated to the pool. Jackpots are explicitly a (large) fraction of the unallocated award funds and so cannot make the lottery operation insolvent— only an excess of fixed-value awards can do that. In fact, the increased sales on rolldown draws just mean more profit for the operators and reduce their biggest risk, which is something happening to the stored funds used to pay out prizes.

sureaboutthis 7y ago

I first read about these people a year or so ago so CBS "news" has finally caught up.

ocfnash 7y ago

A wonderful account of this is given in Ellenberg's "How Not to Be Wrong": https://en.wikipedia.org/wiki/How_Not_to_Be_Wrong https://en.wikipedia.org/wiki/How_Not_to_Be_Wrong I highly recommend the book; it is a popular mathematics book, written by a real mathematician, discussing some real mathematics, with an engaging style.

gauravjain13 7y ago
Video: https://youtu.be/kZTKuMBJP7Y https://youtu.be/kZTKuMBJP7Y

RickJWagner 7y ago

Good for them! Thinking is rewarded.

Xunxi 7y ago

They were featured on 60 minutes twice, including last night. The rendering on Microsoft News is off! You can see the entire video here. https://www.cbsnews.com/news/jerry-and-marge-selbee-how-a-retired-couple-won-millions-using-a-lottery-loophole-60-minutes-2019-06-09/ https://www.cbsnews.com/news/jerry-and-marge-selbee-how-a-re...

js2 7y ago

Previous discussion a year ago: https://news.ycombinator.com/item?id=16494280 https://news.ycombinator.com/item?id=16494280 On this submission: http://highline.huffingtonpost.com/articles/en/lotto-winners/ http://highline.huffingtonpost.com/articles/en/lotto-winners...

joshstrange 7y ago
This is a MUCH better writeup than this recently submitted link. I remember reading it at the time, very well done.
fragmede 7y ago
The original Mass gaming commission report is floating around out there, if anyone is looking for additional reading on this subject, though it is of limited interest, outside of a select few MIT students and a couple from Michigan.

coldcode 7y ago

I wish lotteries handed out many $1M prizes instead of giving $250M to one person. People understand what to do with $1M (I think) but most people are ruined by $250M.

wvenable 7y ago
The reason they don't do that is marketing; more people play for big jackpot. I think even saying there might 250 $1 million winners this week isn't as big of an enticement.
- indigodaddy 7y ago
  Exactly, they would never sell anywhere close to the amount of tickets as they do for the single-winner lump sums that swell to ridiculous amounts. So they wouldn't have the necessary incoming ticket sales to be able to do the 250 $1 million winners.
  - Consultant32452 7y ago
    Around here when the jackpots get high enough you actually find really long lines just to buy tickets. No one lines up to buy the scratch offs with much better odds of winning $1 million.
- vonzeppelin 7y ago
  When the jackpot reached a certain amount, say 500 million, they could switch from a winner takes all to essentially a raffle with 500 winners. I think it would greatly increase the number of tickets purchased when the threshold was met.
  - dawnerd 7y ago
    Isn't that kinda what the Windfall game did more or less?
  - lukeholder 7y ago
    This is what the windfall game in the article did. They were smart enough to buy as many tickets as possible during this raffle.

twic 7y ago

The paper's reporting revealed that two groups were dominating Cash Winfall: the Selbee gang from Evart, Michigan, and their competition, a syndicate led by math majors from MIT, the Massachusetts Institute of Technology. These were kids young enough to be the Selbees' grandchildren. Incredibly, the MIT group bet between $17 and $18 million on Cash Winfall over a seven-year period, earning at least $3.5 million in profits. Almost the exact same rate of return as the Selbees. A nice illustration of the fact that there is only one mathematics, and it's equally available to everyone!

bhl 7y ago
Based on the numbers alone, that's about a 20% return for the MIT group, for an annualized return (not considering compound interest) of less than 3% per year. Does this suggest that those trying to game the lottery should just turn to investing in the market? It's amusing to see that the market, which is less structured in probability and more volatile, outperforms the lottery in this aspect.
- mNovak 7y ago
  The money is only tied up for a few days of the year while they hold tickets though, the rest of the time it could be sitting in a suitably liquid investment. In that sense it far outperforms the market.
- bcbrown 7y ago
  That doesn't mean they had that amount of capital under investment. If you bet $10 every week, and every week you win $11, at the end of the year you've bet $520 and made a profit of $52. But you never had more than $10 "invested". If that $18 million was evenly spread out over 7 years, it would be close to $50k/week, or $215k/month. Those are probably more accurate amounts of working capital for calculating ROI.
  - adrianmonk 7y ago
    Yeah, the way the article phrased it, I have a feeling this is a useless statistic like the sum total of all the money spent on tickets.

unixhero 7y ago

Great story.. but extremely shitty interviewer in my view.

jedberg 7y ago

To all the folks saying, "how did the State not know the odds?", a lot of gambling games come out without anyone running the odds. A great example is blackjack switch [0]. The game was invented by an ex-gambler and he never really knew the odds of the game. He just convinced some casinos to try it and would advertise what their average take was. Because most people are bad at math and wouldn't play well, it was always bigger than the actual house advantage anyway. It was only years later that someone finally ran the numbers and figured out the actual house advantage of the game [1], but no one cared because everyone who had a table was making money on it. Even with regular blackjack, the casinos always make way more than the statistical house advantage because people play poorly. It was probably the same deal here. The State didn't care what they actual odds were, they just cared that they were making money on it. [0] https://en.wikipedia.org/wiki/Blackjack_Switch https://en.wikipedia.org/wiki/Blackjack_Switch [1] https://wizardofodds.com/games/blackjack/switch/ https://wizardofodds.com/games/blackjack/switch/

qtplatypus 7y ago
I work in the gambling industry and live in au. From my perspective this is super strange. By law vendors have to publish the odd (and on some games the EV).
- rwc 7y ago
  Publishing the odds is common. Doing the math on those odds apparently is not.
  - MegaButts 7y ago
    But in order to publish the odds, you have to know the odds. And the only way to know the odds is to do the math, correct? Unless you're making a distinction for determining the odds during optimal play (which makes a lot more sense to me).
    - kijin 7y ago
      Lotteries are required to publish the odds of matching x out of y numbers. Once the design is fixed, this figure does not change. The expected dollar value of a winning ticket, on the other hand, changes every week depending on the number of tickets sold that week as well as the amount of any unclaimed jackpot(s) rolled over from previous weeks. I won't be surprised if state lotteries are not legally required to publish these figures every week. Nobody wants to be held responsible for a precise amount published on Tuesday when a snowstorm on Friday causes ticket sales to plummet. Many states do publish estimates of the jackpot, of course, for advertising purposes. But they're only estimates, and I've never seen estimates of anything other than the jackpot. The Selbees took advantage of smaller winnings that usually go unnoticed.

notfed 7y ago

The title of an article I would never have clicked on if it were not referenced via Hacker News...

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mattdeboard 7y ago

"That was satisfactory." I love that this guy, who is probably, what, 80? 81? pulled off this huge math heist after probably a lifetime spent doing math running a convenience store. I bet it feels great to have that sense of, like, ease with himself in old age, having made a mark on the world in a way that hurt no one and helped a lot of people. He stuck the landing

gowld 7y ago
He hurt all the lottery players he beat.
- zaroth 7y ago
  In fact not. Their winnings did not take a $1 of winnings from anyone else.
- TallGuyShort 7y ago
  They bet money on a game that somebody else played better.

fewrx 7y ago

Every decade or so some "lottery loophole" like this is discovered, exploited, publicized, and rules are updated to close it. I'm curious to see if another loophole resulting in a massive rework of the lottery system will ever present itself, or if the laws and rules have finally prevented that after the last few.

elamje 7y ago

I really enjoyed this story! The best part is people like to think this loop hole is easy “profit”. No one pointed out the fact that they would go on 10 day benders buying/sorting/etc. to get the profit! Even this loop hole for easy profit was incredibly arduous in manual labor.

seventhtiger 7y ago

I was wondering how both these syndicates and the state we winning. I think I understand now. Lotteries are zero sum games so no extra money is being created. All ticket purchases either go to the state or the winners. So if the players have a positive return how can the state also be winning? The players have a positive return only for the rollover round. The players have a negative return for all other rounds, where the state makes its money, and the syndicates don't play. So the people who lost are all the suckers who played in non-rollover rounds.

bamurphymac1 7y ago

Great story. Now they should go make another million or two selling the movie rights!